Purpose <p>Mass irregularities significantly influence the seismic response of structures by amplifying the contributions of higher vibration modes to their dynamic behavior. This underscores the importance of effective control strategies and the identification of optimal damper placements along the structure’s height. This study investigates the placement of Inerter-Connected Tuned Liquid Column Damper (TLCDI) in structures with irregular mass distributions, aiming to develop a comprehensive design graph for practical applications.</p> Methods <p>A novel performance index is introduced to evaluate a ten-story regular building, where mass irregularities were induced at its various heights, including both local and setback types. Thirteen distinct structural configurations are analyzed under 16 earthquake records to assess dynamic responses and evaluate the effectiveness of the control strategies.</p> Results and Conclusions <p>By employing the Monte Carlo simulations and the newly introduced performance index, the study identifies optimal damper placements and effective control strategies. The resulting design graphs provide engineers with practical tools to improve the seismic performance of structures affected by mass irregularities.</p>